Feedback control systems, also known as servomechanisms or servo devices have been developed using a wide variety of technologies and techniques. These systems have a broad spectrum of applications. Many special types of servos are used in high performance equipment. A special type of servo loop acting to achieve proportional, integral and differential (PID) compensation is often used to processes an error signal and generate a command. The goal of this loop is to generate the proper command to ultimately drive the error signal to zero. The command generated by the PID compensator consists of three components.                1. The component proportional to the error (proportional P).        2. The component proportional to the cumulative sum of the error (integral I).        3. The component proportional to the rate of change of the error (derivative D).        
Consider the case where the error is a position error. The task of the PID compensator is to drive the servomechanism to a commanded position, thus reducing the position error to zero. The design of the proper PID compensator is well-known to practitioners in the field of control systems and the details of such design approaches are not the major focus of this invention. Conventional design techniques assure that the design is stable with appropriate stability margins. Digital servos are increasingly common because they are very effective due to development in recent years.
When a design is implemented considerations must be given to factors such as mechanical, electrical and timing limits. These limits may be exceeded if the mechanism moves too quickly. An example, is when the compensator generates a command to a very fast actuator and the loop must have a large bandwidth to hold the position in the presence of high frequency disturbances. Such devices work well when the position error is small and all techniques have been brought to bear to overcome these disturbances. Consider, what happens when a new position command is issued. The position error is very large resulting in an extremely large component of proportional correction signal. This results in a large correction command given to the actuator driver that tends to cause correction. The integral component also begins changing but its effect is not as immediate. The derivative component is an impulse because the rate of change of the position error is large. In a prior art design a high performance actuator can quickly reach high speeds.
FIG. 1 illustrates the components of a prior art PID compensator. The control equations are easily recognized in FIG. 1. The input signal is position error 100. The output signal is torque command 110. The proportional signal couples position error 100 to summing junction 103. The integrate signal comes from integration block 101 and the modifying gain constant factor W1 in amplifier block 102. The signal operation comes from derivative block 105, the modifying gain constant factor 1/W2 in amplifier block 106, low pass filter 107 having a cutoff frequency of W3 and low pass filter 108 having a cutoff frequency of W4. The transfer function frequency characteristics are shaped at low frequencies through parameters W1 and W2 and by parameters W3 and W4 at high frequency.
There is need to introduce a moderating factor in the servo operation to prevent unwarranted over-drive of the high performance actuator. The PID compensator of FIG. 1 may be described mathematically by transfer function equation [1] which omits W3 and W4 for simplicity:                                           H            0                    ⁡                      (            s            )                          =                  1          +                                    w              1                        s                    +                      s                          w              2                                                          [        1        ]            
FIG. 2 illustrates a piece-wise graphical representation of the PID compensator of FIG. 1 and Equation 1 with an arbitrary overall gain. The integral portion 200 removes low frequency offsets (DC bias) and the derivative portion 207 provides fast response to high frequency disturbances. The proportional portion 205 bridges the integral and derivative regions. FIG. 2 also illustrates the derivative poles, W3 203 and W4 204 for the typical PID compensator illustrated in FIG. 1. In FIG. 2, the lower frequency break points W1 201 and W2 202 of the transfer function versus frequency are introduced by the frequency responses of respective amplification stages 102 and 106. Since the differentiator is the dominant component at frequencies above W2 202, the poles W3 203 and W4 can be included in the implementation without affecting the validity of the approaches to be described here.